PLANCK’S QUANTUM THEORY OF BLACK BODY RADIATION
The findings in the black body radiation led Max plank in 1901 to postulate that radiant energy is quantized i.e. it is radiated in form of energy packets.
BASIC POSTULATES OF THE PLANK’S THEORY
1. Any radiation is associated with energy.
2. Radiant energy is emitted or absorbed in small packets known as quanta.
3. The energy associated with a quantum is proportional to the frequency f of the radiation
4. The energy is absorbed or emitted only in whole number of quanta
Black Body Radiation
A blackbody is a substance that absorbs all light fall on it and does not reflect any light.
It is not easy to get a black body however a sealed metal box with a very small hole on it is very close to a black body.
From law of physics it follows that a good absorber of radiation also is a good radiator. A black body is supposed to be the best radiator.
When a black body is heated it emits light. The colour of light emitted changes from red to yellow then to white as the temperature is increased.
The change in colour with temperature shows that the frequency changes with temperature.
This in contradiction with the classical wave theory since in the classical wave theory energy is uniformly distributed over the wave form when heating the black body the colour of radiation should stay the same
Only the intensity is supposed to increase with temperature.
DISTRIBUTION OF ENERGY IN THE SPECTRUM OF A BLACK BODY
Lamer and Pringshein investigated the distribution of energy amongst the different wavelength of a thermal spectrum of a back body radiation
The results obtained by Lamer and Pringshein are shown in figure below
Results:
1. At a given temperature the energy is not uniformly distributed in the radiation spectrum of a hot body
2. At a given temperature the intensity of radiations increases with increased in wavelength and at a particular wavelength λ its value is maximum with further increase in wavelength the intensity of heat radiations decreased
3. With increase in temperature wave length increases, wavelength emission of energy takes place.
The points on the dotted line represent wavelength at various temperatures
4. For all wavelength an increase in temperature causes an increase in the energy emission The area under each curve represents the total energy emitted for the complete spectrum at a particular temperature
5. This area increases in temperature of the body. It is found that the area is directly proportional to fourth power of the temperature of the body
This represents Stefan’s Boltzmann’s law.
Plank’s constant
Plank’s constant is a fundamental constant equal to the ratio of the quantum energy to the frequency of the radiation.
ELECTRON EMISSION
This is the liberation of electron from the surface of a substance.
For electron emission metals are used because they have many free electrons.
If a piece of metal is investigated at room
temperature the random motion of free electrons is as shown in figure below
temperature the random motion of free electrons is as shown in figure below
However these electrons are free only to the extent that they may transfer from one atom to another within the metal but they cannot leave the metal surface to provide electron emission.
It is because the free electron that start at the surface of metal find behind them positive nuclei pulling them back and none pulling forward.
This at the surface of a metal a free electron encounters force that prevents it to leave the metal
It is because the free electron that start at the surface of metal find behind them positive nuclei pulling them back and none pulling forward.
This at the surface of a metal a free electron encounters force that prevents it to leave the metal
In other words the metallic surface offers a barrier to free electrons and is known as surface barriers
However if sufficient external energy is given to the free electron its kinetic energy is increased and thus electron will cross over the surface barrier to leave the metal.
WORK FUNCTION OF THE METAL
WORK FUNCTION OF THE METAL
This is the additional energy required by an electron to overcome the surface barrier of the metal.
Or
This is the minimum energy required by an electron to just escape from the metal surface.
The work function depends on
i) Nature of metal
ii) Conditions of the metal surface
It is measured by a smaller unit of energy called electron volt. (eV) because this is the conventional unit of energy i.e. joule is very large for computations in atomic and nuclear physics.
Electron volt.
One electron volt is the amount of energy acquired by an electron when it is accelerated through a potential difference of IV
Since potential difference V
Work done = QV
For an electron
The electron volt is the kinetic energy gained by an electron being accelerated by a potential difference of one volt.
The work function of pure metal varies roughly from V to V as shown in table below
V to 
V as shown in table belowMetal | Work Function Wo (eV) |
Cs | 2.14 |
K | 2.30 |
Na | 2.75 |
Ca | 3.20 |
Mo | 4.17 |
Pb | 4.25 |
Al | 4.28 |
Hg | 4.49 |
Cu | 4.65 |
Ag | 4.70 |
Ni | 5.15 |
Pt | 5.65 |
It is clear from the table above that the work function of platinum is the highest while it is lowest for Cesium.
It is desirable that metal used for electron emission should have low work function so that a small amount of energy is required to cause emission of electrons
PHOTOELECTRIC EFFECT
Photoelctric effect is the phenomenon of emission of electron from a metallic surface when radiation of suitable frequency falls on it or is the phenomenon where electromagnetic radiation of certain frequency when incident on certain material liberates electron from the surface of the material.
Photo emission
Photo emission is the emission of electron by electromagnetic radiation.
Photo electrons
These are emitted or rejected electrons from the surface of the cathode.
Photo electric effect is a general phenomenon exhibited by all substances but is most easily observed with metals.
When radiation of suitable frequency the thres
hold frequency is incident on a metallic surface electrons are emitted from the metal surface.
hold frequency is incident on a metallic surface electrons are emitted from the metal surface.
The threshold frequency is different for metals.
Certain alkali, metals e.g. sodium potassium, calcium show photo electric effect when visible light falls on them.
However, metal like zinc, calcium, magnesium etc show photo electric effect to ultra violet light.
Threshold Frequency
The threshold frequency is the minimum frequency of the incident radiation which is just sufficient to eject photo electron from surface of a metal Or is the minimum frequency of radiation below which no photo electron emission occurs.
It is denoted by
Illuminating a metal surface with light of frequency less than will not cause ejection of photo electrons, no matter now great is the intensity of radiation.
will not cause ejection of photo electrons, no matter now great is the intensity of radiation.But illumination with a frequency greater than causes emission of photo electrons even if the radiation intensity is very small
causes emission of photo electrons even if the radiation intensity is very small Threshold wavelength
The threshold wavelength is the maximum wavelength of the incident radiation at which photo electric emission occurs.
It is the wavelength corresponding to threshold frequency
If the wavelength of the incident radiation is greater than threshold wavelength then there will be no photo electric emission.
Photoelectric current is the photo-electrons emitted per second
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